Secant Method Example: Solution for Equation

Find the solution of the following equation using the secant method:

secant method

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Write a Python 3 code for this method.

Solution

Hand solution

Let’s choose the initial values of x:

secant method example

Plugging the above values into the equation, we get:

secant method sample

The formula for finding the next x values is:

secant method formula

Now, we can find the

 

  \[x_{2}\]

 

value:

secant method formula example

Changing x for the

 

  \[x_{2}\]

 

value:

secant method formula sample

Repeating the above steps, we will find the next x values:

secant method formula assignment

secant method python

secant method python example

 

is the root of the equation.

Python 3 Code

Let’s define a function for our equation first:

secant method example
Knowing the formula for finding the next values of x, we can write a function for it too:

Now, it’s time to write our main function for finding the root of the equation. As we should choose two initial values for x, our function should accept two initial parameters:


Now, let’s find the corresponding y values:


To simplify things, we will use current and previous values (xc, yc, xp, yp):


And let’s repeat the above steps in a while loop. In order to prevent an infinite loop, we need to add an exit condition. In our case we will check if the absolute value of y is larger than the 0.001 threshold:

At last, the found x value is returned:

The entire code:

secant method example

secant method example

secant method example

Secant method is one of the root-finding algorithms. You can solve equations using this method by hand and with the help of Python code. Here, you can find both secant method examples provided by one of our experts.

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